Find each product or quotient where possible. See Example 2. -5⁄2 ( 12⁄15 )

Verified step by step guidance

1. Identify the problem as a multiplication of two fractions: \(-\frac{5}{2} \times \frac{12}{15}\).
2. Multiply the numerators together: \(-5 \times 12\) and multiply the denominators together: \(2 \times 15\) to get a new fraction.
3. Write the product as \(\frac{-5 \times 12}{2 \times 15}\), which simplifies to \(\frac{-60}{30}\) before reducing.
4. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD).
5. Express the simplified fraction as the final product of the multiplication.

Key Concepts

Multiplication of Fractions

To multiply fractions, multiply the numerators together and the denominators together. For example, (a/b) × (c/d) = (a×c)/(b×d). This rule applies to both positive and negative fractions.

Simplifying Fractions

After multiplying, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). Simplification makes the fraction easier to interpret and use.

Handling Negative Signs in Multiplication

When multiplying fractions, a negative sign in either fraction affects the product's sign. Multiplying a negative by a positive yields a negative result, while multiplying two negatives yields a positive result.